Physics Chapter on Simple Harmonic Motion

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Questions and Answers

What is the impact of superimposing two collinear simple harmonic motions with nearly equal frequencies?

They will produce a random motion that lacks a defined pattern.
They will completely cancel each other out.
They will create a resultant motion that can vary in amplitude. (correct)
They will result in a uniform motion without variation.

How does the amplitude of the resultant motion vary when two simple harmonic motions of different amplitudes are combined?

The amplitude remains constant regardless of individual amplitudes.
The amplitude becomes the average of the two original amplitudes.
The resultant amplitude equals one of the original amplitudes.
The amplitude varies between the difference and sum of the two amplitudes. (correct)

What phenomenon results from the superposition of two harmonic motions with slight frequency differences?

Linear superposition leading to a single wave
Dissipation of energy
Constructive and destructive interference creating beats (correct)
Formation of a stationary wave pattern

Which statement best describes the formation of beats in superimposed harmonic motions?

Beats are perceived as fluctuations in amplitude due to frequency differences. (C) Signup and view all the answers

In the context of beats, what role does the frequency difference between two harmonic motions play?

The beat frequency is determined by the absolute difference of the two frequencies. (D) Signup and view all the answers

What is the resultant equation when two collinear simple harmonic motions of frequencies $f_1$ and $f_2$ are superimposed?

The resultant equation can be expressed as $y = A_1 ext{sin}(ω_1 t + φ_1) + A_2 ext{sin}(ω_2 t + φ_2)$, where $A_1$ and $A_2$ are the amplitudes, $ω_1$ and $ω_2$ are the angular frequencies, and $φ_1$ and $φ_2$ are the phase constants. Signup and view all the answers

Explain how beats are formed when two simple harmonic motions with nearly equal frequencies are combined.

Beats are formed due to the periodic constructive and destructive interference of the two waves, resulting from the slight difference in their frequencies, leading to variations in amplitude over time. Signup and view all the answers

What role does the frequency difference play in the frequency of beats produced?

The frequency of beats is equal to the absolute difference between the two frequencies, expressed as $f_{beat} = |f_1 - f_2|$. Signup and view all the answers

How does the amplitude of the resultant motion relate to the individual amplitudes of the two simple harmonic motions?

The amplitude of the resultant motion varies between $|A_1 - A_2|$ and $|A_1 + A_2|$, resulting in a modulation of loudness seen in the beat phenomenon. Signup and view all the answers

What conditions are necessary for the clear formation of beats in superimposed harmonic motions?

For clear beats to form, the two harmonic motions must have nearly equal frequencies and should not differ too significantly in amplitude. Signup and view all the answers

Flashcards

Superimposed SHMs

Two simple harmonic motions combined to form a resultant motion.

Nearly equal frequencies

The frequencies of the two SHMs are very close to each other.